LMFDB - Embedded newform 5819.2.a.u.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5819,2,Mod(1,5819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5819, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5819.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5819 = 11 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5819.a (trivial)

Newform invariants

comment:select newform

sage:traces = [60,5,9,73,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$46.4649489362$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 253)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	5819.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.05610 q^{2} -2.21869 q^{3} +2.22755 q^{4} -4.33173 q^{5} +4.56186 q^{6} +2.89005 q^{7} -0.467865 q^{8} +1.92260 q^{9} +8.90647 q^{10} +1.00000 q^{11} -4.94225 q^{12} +3.80993 q^{13} -5.94222 q^{14} +9.61078 q^{15} -3.49312 q^{16} -6.41271 q^{17} -3.95307 q^{18} -1.52667 q^{19} -9.64914 q^{20} -6.41213 q^{21} -2.05610 q^{22} +1.03805 q^{24} +13.7639 q^{25} -7.83361 q^{26} +2.39041 q^{27} +6.43772 q^{28} +1.72451 q^{29} -19.7607 q^{30} +5.22427 q^{31} +8.11794 q^{32} -2.21869 q^{33} +13.1852 q^{34} -12.5189 q^{35} +4.28270 q^{36} +7.05826 q^{37} +3.13899 q^{38} -8.45308 q^{39} +2.02667 q^{40} +2.45336 q^{41} +13.1840 q^{42} +2.96049 q^{43} +2.22755 q^{44} -8.32819 q^{45} +6.98634 q^{47} +7.75017 q^{48} +1.35236 q^{49} -28.2999 q^{50} +14.2278 q^{51} +8.48682 q^{52} +1.45325 q^{53} -4.91493 q^{54} -4.33173 q^{55} -1.35215 q^{56} +3.38722 q^{57} -3.54577 q^{58} +13.8389 q^{59} +21.4085 q^{60} -2.81307 q^{61} -10.7416 q^{62} +5.55641 q^{63} -9.70506 q^{64} -16.5036 q^{65} +4.56186 q^{66} +5.36304 q^{67} -14.2846 q^{68} +25.7401 q^{70} +0.660274 q^{71} -0.899520 q^{72} +11.2357 q^{73} -14.5125 q^{74} -30.5378 q^{75} -3.40074 q^{76} +2.89005 q^{77} +17.3804 q^{78} +8.74672 q^{79} +15.1312 q^{80} -11.0714 q^{81} -5.04435 q^{82} -0.901787 q^{83} -14.2833 q^{84} +27.7781 q^{85} -6.08707 q^{86} -3.82616 q^{87} -0.467865 q^{88} -3.38269 q^{89} +17.1236 q^{90} +11.0109 q^{91} -11.5911 q^{93} -14.3646 q^{94} +6.61313 q^{95} -18.0112 q^{96} +2.65813 q^{97} -2.78060 q^{98} +1.92260 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) $ 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 + 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 - 7 * q^10 + 60 * q^11 + 41 * q^12 + 46 * q^13 + 16 * q^14 + 4 * q^15 + 99 * q^16 - 5 * q^17 + 36 * q^18 - 8 * q^19 + 82 * q^20 - 13 * q^21 + 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 - 29 * q^28 + 42 * q^29 - 14 * q^30 + 71 * q^31 + 40 * q^32 + 9 * q^33 + 10 * q^34 + 9 * q^35 + 93 * q^36 - 5 * q^37 - 11 * q^38 + 56 * q^39 - 40 * q^40 + 62 * q^41 + 43 * q^42 - 2 * q^43 + 73 * q^44 - q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 - 27 * q^51 + 102 * q^52 + 11 * q^53 + 69 * q^54 + 8 * q^55 + 13 * q^56 + 38 * q^57 + 58 * q^58 + 57 * q^59 - 49 * q^60 - 26 * q^61 + 17 * q^62 - 41 * q^63 + 184 * q^64 - 19 * q^65 + 26 * q^66 + 7 * q^67 - 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 - 63 * q^74 + q^75 - 42 * q^76 - 3 * q^78 - 25 * q^79 + 148 * q^80 + 68 * q^81 + 59 * q^82 - 41 * q^83 - 97 * q^84 + 160 * q^85 + 78 * q^86 + 41 * q^87 + 30 * q^88 + 51 * q^89 - 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 - 13 * q^97 - 75 * q^98 + 75 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.05610	−1.45388	−0.726941	−	0.686700i	$-0.759059\pi$
$2$	−2.05610	−1.45388	−0.726941	+	0.686700i	$0.759059\pi$
$3$	−2.21869	−1.28096	−0.640482	−	0.767973i	$-0.721265\pi$
$3$	−2.21869	−1.28096	−0.640482	+	0.767973i	$0.721265\pi$
$4$	2.22755	1.11377
$5$	−4.33173	−1.93721	−0.968604	−	0.248610i	$-0.920026\pi$
$5$	−4.33173	−1.93721	−0.968604	+	0.248610i	$0.920026\pi$
$6$	4.56186	1.86237
$7$	2.89005	1.09233	0.546167	−	0.837676i	$-0.316086\pi$
$7$	2.89005	1.09233	0.546167	+	0.837676i	$0.316086\pi$
$8$	−0.467865	−0.165415
$9$	1.92260	0.640868
$10$	8.90647	2.81647
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.94225	−1.42671
$13$	3.80993	1.05669	0.528343	−	0.849031i	$-0.322814\pi$
$13$	3.80993	1.05669	0.528343	+	0.849031i	$0.322814\pi$
$14$	−5.94222	−1.58813
$15$	9.61078	2.48149
$16$	−3.49312	−0.873280
$17$	−6.41271	−1.55531	−0.777655	−	0.628691i	$-0.783591\pi$
$17$	−6.41271	−1.55531	−0.777655	+	0.628691i	$0.783591\pi$
$18$	−3.95307	−0.931747
$19$	−1.52667	−0.350243	−0.175121	−	0.984547i	$-0.556032\pi$
$19$	−1.52667	−0.350243	−0.175121	+	0.984547i	$0.556032\pi$
$20$	−9.64914	−2.15761
$21$	−6.41213	−1.39924
$22$	−2.05610	−0.438362
$23$	0	0
$23$	0	0
$24$	1.03805	0.211891
$25$	13.7639	2.75277
$26$	−7.83361	−1.53630
$27$	2.39041	0.460035
$28$	6.43772	1.21661
$29$	1.72451	0.320234	0.160117	−	0.987098i	$-0.448813\pi$
$29$	1.72451	0.320234	0.160117	+	0.987098i	$0.448813\pi$
$30$	−19.7607	−3.60780
$31$	5.22427	0.938306	0.469153	−	0.883117i	$-0.344559\pi$
$31$	5.22427	0.938306	0.469153	+	0.883117i	$0.344559\pi$
$32$	8.11794	1.43506
$33$	−2.21869	−0.386225
$34$	13.1852	2.26124
$35$	−12.5189	−2.11608
$36$	4.28270	0.713783
$37$	7.05826	1.16037	0.580186	−	0.814484i	$-0.302980\pi$
$37$	7.05826	1.16037	0.580186	+	0.814484i	$0.302980\pi$
$38$	3.13899	0.509212
$39$	−8.45308	−1.35358
$40$	2.02667	0.320444
$41$	2.45336	0.383150	0.191575	−	0.981478i	$-0.438640\pi$
$41$	2.45336	0.383150	0.191575	+	0.981478i	$0.438640\pi$
$42$	13.1840	2.03433
$43$	2.96049	0.451471	0.225735	−	0.974189i	$-0.427521\pi$
$43$	2.96049	0.451471	0.225735	+	0.974189i	$0.427521\pi$
$44$	2.22755	0.335816
$45$	−8.32819	−1.24149
$46$	0	0
$47$	6.98634	1.01906	0.509531	−	0.860452i	$-0.329819\pi$
$47$	6.98634	1.01906	0.509531	+	0.860452i	$0.329819\pi$
$48$	7.75017	1.11864
$49$	1.35236	0.193195
$50$	−28.2999	−4.00221
$51$	14.2278	1.99230
$52$	8.48682	1.17691
$53$	1.45325	0.199619	0.0998096	−	0.995007i	$-0.468177\pi$
$53$	1.45325	0.199619	0.0998096	+	0.995007i	$0.468177\pi$
$54$	−4.91493	−0.668837
$55$	−4.33173	−0.584090
$56$	−1.35215	−0.180689
$57$	3.38722	0.448648
$58$	−3.54577	−0.465582
$59$	13.8389	1.80168	0.900838	−	0.434156i	$-0.142953\pi$
$59$	13.8389	1.80168	0.900838	+	0.434156i	$0.142953\pi$
$60$	21.4085	2.76382
$61$	−2.81307	−0.360176	−0.180088	−	0.983650i	$-0.557638\pi$
$61$	−2.81307	−0.360176	−0.180088	+	0.983650i	$0.557638\pi$
$62$	−10.7416	−1.36419
$63$	5.55641	0.700042
$64$	−9.70506	−1.21313
$65$	−16.5036	−2.04702
$66$	4.56186	0.561526
$67$	5.36304	0.655200	0.327600	−	0.944817i	$-0.393760\pi$
$67$	5.36304	0.655200	0.327600	+	0.944817i	$0.393760\pi$
$68$	−14.2846	−1.73227
$69$	0	0
$70$	25.7401	3.07653
$71$	0.660274	0.0783601	0.0391800	−	0.999232i	$-0.487525\pi$
$71$	0.660274	0.0783601	0.0391800	+	0.999232i	$0.487525\pi$
$72$	−0.899520	−0.106009
$73$	11.2357	1.31504	0.657519	−	0.753438i	$-0.271606\pi$
$73$	11.2357	1.31504	0.657519	+	0.753438i	$0.271606\pi$
$74$	−14.5125	−1.68704
$75$	−30.5378	−3.52620
$76$	−3.40074	−0.390091
$77$	2.89005	0.329351
$78$	17.3804	1.96794
$79$	8.74672	0.984083	0.492042	−	0.870572i	$-0.336251\pi$
$79$	8.74672	0.984083	0.492042	+	0.870572i	$0.336251\pi$
$80$	15.1312	1.69172
$81$	−11.0714	−1.23016
$82$	−5.04435	−0.557055
$83$	−0.901787	−0.0989840	−0.0494920	−	0.998775i	$-0.515760\pi$
$83$	−0.901787	−0.0989840	−0.0494920	+	0.998775i	$0.515760\pi$
$84$	−14.2833	−1.55844
$85$	27.7781	3.01296
$86$	−6.08707	−0.656386
$87$	−3.82616	−0.410208
$88$	−0.467865	−0.0498746
$89$	−3.38269	−0.358565	−0.179282	−	0.983798i	$-0.557378\pi$
$89$	−3.38269	−0.358565	−0.179282	+	0.983798i	$0.557378\pi$
$90$	17.1236	1.80499
$91$	11.0109	1.15425
$92$	0	0
$93$	−11.5911	−1.20194
$94$	−14.3646	−1.48160
$95$	6.61313	0.678492
$96$	−18.0112	−1.83826
$97$	2.65813	0.269892	0.134946	−	0.990853i	$-0.456914\pi$
$97$	2.65813	0.269892	0.134946	+	0.990853i	$0.456914\pi$
$98$	−2.78060	−0.280883
$99$	1.92260	0.193229
$100$	30.6597	3.06597
$101$	3.58924	0.357143	0.178571	−	0.983927i	$-0.442852\pi$
$101$	3.58924	0.357143	0.178571	+	0.983927i	$0.442852\pi$
$102$	−29.2539	−2.89656
$103$	−8.13818	−0.801879	−0.400939	−	0.916105i	$-0.631316\pi$
$103$	−8.13818	−0.801879	−0.400939	+	0.916105i	$0.631316\pi$
$104$	−1.78254	−0.174792
$105$	27.7756	2.71062
$106$	−2.98803	−0.290223
$107$	−2.75678	−0.266508	−0.133254	−	0.991082i	$-0.542543\pi$
$107$	−2.75678	−0.266508	−0.133254	+	0.991082i	$0.542543\pi$
$108$	5.32476	0.512376
$109$	−9.71977	−0.930985	−0.465493	−	0.885052i	$-0.654123\pi$
$109$	−9.71977	−0.930985	−0.465493	+	0.885052i	$0.654123\pi$
$110$	8.90647	0.849198
$111$	−15.6601	−1.48639
$112$	−10.0953	−0.953914
$113$	−11.3012	−1.06312	−0.531562	−	0.847019i	$-0.678395\pi$
$113$	−11.3012	−1.06312	−0.531562	+	0.847019i	$0.678395\pi$
$114$	−6.96446	−0.652282
$115$	0	0
$116$	3.84144	0.356668
$117$	7.32499	0.677196
$118$	−28.4542	−2.61942
$119$	−18.5330	−1.69892
$120$	−4.49655	−0.410477
$121$	1.00000	0.0909091
$122$	5.78395	0.523654
$123$	−5.44325	−0.490801
$124$	11.6373	1.04506
$125$	−37.9626	−3.39548
$126$	−11.4245	−1.01778
$127$	−14.4321	−1.28064	−0.640319	−	0.768109i	$-0.721198\pi$
$127$	−14.4321	−1.28064	−0.640319	+	0.768109i	$0.721198\pi$
$128$	3.71870	0.328690
$129$	−6.56843	−0.578318
$130$	33.9331	2.97613
$131$	7.41846	0.648154	0.324077	−	0.946031i	$-0.394946\pi$
$131$	7.41846	0.648154	0.324077	+	0.946031i	$0.394946\pi$
$132$	−4.94225	−0.430168
$133$	−4.41215	−0.382582
$134$	−11.0270	−0.952584
$135$	−10.3546	−0.891183
$136$	3.00028	0.257272
$137$	4.41814	0.377467	0.188733	−	0.982028i	$-0.439562\pi$
$137$	4.41814	0.377467	0.188733	+	0.982028i	$0.439562\pi$
$138$	0	0
$139$	−0.359835	−0.0305208	−0.0152604	−	0.999884i	$-0.504858\pi$
$139$	−0.359835	−0.0305208	−0.0152604	+	0.999884i	$0.504858\pi$
$140$	−27.8864	−2.35684
$141$	−15.5006	−1.30538
$142$	−1.35759	−0.113926
$143$	3.80993	0.318603
$144$	−6.71589	−0.559657
$145$	−7.47011	−0.620359
$146$	−23.1017	−1.91191
$147$	−3.00048	−0.247476
$148$	15.7226	1.29239
$149$	−12.9573	−1.06151	−0.530754	−	0.847526i	$-0.678091\pi$
$149$	−12.9573	−1.06151	−0.530754	+	0.847526i	$0.678091\pi$
$150$	62.7888	5.12668
$151$	−5.04818	−0.410815	−0.205408	−	0.978677i	$-0.565852\pi$
$151$	−5.04818	−0.410815	−0.205408	+	0.978677i	$0.565852\pi$
$152$	0.714277	0.0579355
$153$	−12.3291	−0.996748
$154$	−5.94222	−0.478838
$155$	−22.6301	−1.81769
$156$	−18.8297	−1.50758
$157$	12.9516	1.03365	0.516823	−	0.856092i	$-0.327114\pi$
$157$	12.9516	1.03365	0.516823	+	0.856092i	$0.327114\pi$
$158$	−17.9841	−1.43074
$159$	−3.22432	−0.255705
$160$	−35.1647	−2.78001
$161$	0	0
$162$	22.7639	1.78850
$163$	−16.6852	−1.30689	−0.653444	−	0.756974i	$-0.726677\pi$
$163$	−16.6852	−1.30689	−0.653444	+	0.756974i	$0.726677\pi$
$164$	5.46498	0.426743
$165$	9.61078	0.748198
$166$	1.85417	0.143911
$167$	−6.79567	−0.525865	−0.262932	−	0.964814i	$-0.584690\pi$
$167$	−6.79567	−0.525865	−0.262932	+	0.964814i	$0.584690\pi$
$168$	3.00001	0.231456
$169$	1.51560	0.116585
$170$	−57.1146	−4.38049
$171$	−2.93518	−0.224459
$172$	6.59465	0.502837
$173$	12.4784	0.948713	0.474356	−	0.880333i	$-0.342681\pi$
$173$	12.4784	0.948713	0.474356	+	0.880333i	$0.342681\pi$
$174$	7.86698	0.596394
$175$	39.7782	3.00695
$176$	−3.49312	−0.263304
$177$	−30.7044	−2.30788
$178$	6.95516	0.521311
$179$	16.5404	1.23629	0.618143	−	0.786066i	$-0.287885\pi$
$179$	16.5404	1.23629	0.618143	+	0.786066i	$0.287885\pi$
$180$	−18.5515	−1.38274
$181$	17.9548	1.33457	0.667283	−	0.744804i	$-0.267457\pi$
$181$	17.9548	1.33457	0.667283	+	0.744804i	$0.267457\pi$
$182$	−22.6395	−1.67815
$183$	6.24134	0.461373
$184$	0	0
$185$	−30.5745	−2.24788
$186$	23.8324	1.74747
$187$	−6.41271	−0.468944
$188$	15.5624	1.13501
$189$	6.90840	0.502512
$190$	−13.5973	−0.986448
$191$	2.27349	0.164504	0.0822520	−	0.996612i	$-0.473789\pi$
$191$	2.27349	0.164504	0.0822520	+	0.996612i	$0.473789\pi$
$192$	21.5326	1.55398
$193$	−21.1289	−1.52089	−0.760444	−	0.649403i	$-0.775019\pi$
$193$	−21.1289	−1.52089	−0.760444	+	0.649403i	$0.775019\pi$
$194$	−5.46538	−0.392391
$195$	36.6164	2.62216
$196$	3.01246	0.215176
$197$	−11.7109	−0.834370	−0.417185	−	0.908822i	$-0.636983\pi$
$197$	−11.7109	−0.834370	−0.417185	+	0.908822i	$0.636983\pi$
$198$	−3.95307	−0.280932
$199$	20.1956	1.43163	0.715815	−	0.698290i	$-0.246055\pi$
$199$	20.1956	1.43163	0.715815	+	0.698290i	$0.246055\pi$
$200$	−6.43963	−0.455351
$201$	−11.8990	−0.839287
$202$	−7.37984	−0.519244
$203$	4.98392	0.349802
$204$	31.6932	2.21897
$205$	−10.6273	−0.742241
$206$	16.7329	1.16584
$207$	0	0
$208$	−13.3086	−0.922783
$209$	−1.52667	−0.105602
$210$	−57.1094	−3.94092
$211$	17.4475	1.20113	0.600566	−	0.799575i	$-0.294942\pi$
$211$	17.4475	1.20113	0.600566	+	0.799575i	$0.294942\pi$
$212$	3.23719	0.222331
$213$	−1.46495	−0.100376
$214$	5.66823	0.387472
$215$	−12.8240	−0.874593
$216$	−1.11839	−0.0760969
$217$	15.0984	1.02494
$218$	19.9848	1.35354
$219$	−24.9286	−1.68452
$220$	−9.64914	−0.650545
$221$	−24.4320	−1.64347
$222$	32.1988	2.16104
$223$	−11.2915	−0.756132	−0.378066	−	0.925779i	$-0.623411\pi$
$223$	−11.2915	−0.756132	−0.378066	+	0.925779i	$0.623411\pi$
$224$	23.4612	1.56757
$225$	26.4624	1.76416
$226$	23.2363	1.54566
$227$	10.2367	0.679436	0.339718	−	0.940527i	$-0.389668\pi$
$227$	10.2367	0.679436	0.339718	+	0.940527i	$0.389668\pi$
$228$	7.54520	0.499693
$229$	−4.45586	−0.294452	−0.147226	−	0.989103i	$-0.547034\pi$
$229$	−4.45586	−0.294452	−0.147226	+	0.989103i	$0.547034\pi$
$230$	0	0
$231$	−6.41213	−0.421887
$232$	−0.806839	−0.0529716
$233$	−11.3574	−0.744050	−0.372025	−	0.928223i	$-0.621336\pi$
$233$	−11.3574	−0.744050	−0.372025	+	0.928223i	$0.621336\pi$
$234$	−15.0609	−0.984563
$235$	−30.2629	−1.97414
$236$	30.8269	2.00666
$237$	−19.4063	−1.26058
$238$	38.1058	2.47003
$239$	15.8082	1.02255	0.511275	−	0.859417i	$-0.329173\pi$
$239$	15.8082	1.02255	0.511275	+	0.859417i	$0.329173\pi$
$240$	−33.5716	−2.16704
$241$	−2.99569	−0.192969	−0.0964847	−	0.995334i	$-0.530760\pi$
$241$	−2.99569	−0.192969	−0.0964847	+	0.995334i	$0.530760\pi$
$242$	−2.05610	−0.132171
$243$	17.3928	1.11575
$244$	−6.26625	−0.401156
$245$	−5.85807	−0.374258
$246$	11.1919	0.713568
$247$	−5.81652	−0.370096
$248$	−2.44425	−0.155210
$249$	2.00079	0.126795
$250$	78.0550	4.93663
$251$	−4.03716	−0.254823	−0.127412	−	0.991850i	$-0.540667\pi$
$251$	−4.03716	−0.254823	−0.127412	+	0.991850i	$0.540667\pi$
$252$	12.3772	0.779689
$253$	0	0
$254$	29.6738	1.86190
$255$	−61.6311	−3.85949
$256$	11.7641	0.735256
$257$	−4.95896	−0.309331	−0.154666	−	0.987967i	$-0.549430\pi$
$257$	−4.95896	−0.309331	−0.154666	+	0.987967i	$0.549430\pi$
$258$	13.5054	0.840806
$259$	20.3987	1.26751
$260$	−36.7626	−2.27992
$261$	3.31555	0.205228
$262$	−15.2531	−0.942340
$263$	10.3871	0.640497	0.320249	−	0.947334i	$-0.396234\pi$
$263$	10.3871	0.640497	0.320249	+	0.947334i	$0.396234\pi$
$264$	1.03805	0.0638876
$265$	−6.29508	−0.386704
$266$	9.07183	0.556229
$267$	7.50516	0.459309
$268$	11.9464	0.729745
$269$	−24.6684	−1.50406	−0.752029	−	0.659130i	$-0.770925\pi$
$269$	−24.6684	−1.50406	−0.752029	+	0.659130i	$0.770925\pi$
$270$	21.2901	1.29568
$271$	10.4042	0.632007	0.316004	−	0.948758i	$-0.397659\pi$
$271$	10.4042	0.632007	0.316004	+	0.948758i	$0.397659\pi$
$272$	22.4004	1.35822
$273$	−24.4298	−1.47856
$274$	−9.08414	−0.548793
$275$	13.7639	0.829992
$276$	0	0
$277$	13.8144	0.830029	0.415015	−	0.909815i	$-0.363776\pi$
$277$	13.8144	0.830029	0.415015	+	0.909815i	$0.363776\pi$
$278$	0.739857	0.0443736
$279$	10.0442	0.601330
$280$	5.85716	0.350032
$281$	−17.9297	−1.06959	−0.534797	−	0.844980i	$-0.679612\pi$
$281$	−17.9297	−1.06959	−0.534797	+	0.844980i	$0.679612\pi$
$282$	31.8707	1.89787
$283$	23.8691	1.41887	0.709434	−	0.704772i	$-0.248951\pi$
$283$	23.8691	1.41887	0.709434	+	0.704772i	$0.248951\pi$
$284$	1.47079	0.0872755
$285$	−14.6725	−0.869124
$286$	−7.83361	−0.463211
$287$	7.09032	0.418528
$288$	15.6076	0.919686
$289$	24.1228	1.41899
$290$	15.3593	0.901929
$291$	−5.89757	−0.345722
$292$	25.0281	1.46466
$293$	32.6407	1.90689	0.953445	−	0.301568i	$-0.0975102\pi$
$293$	32.6407	1.90689	0.953445	+	0.301568i	$0.0975102\pi$
$294$	6.16929	0.359800
$295$	−59.9465	−3.49022
$296$	−3.30232	−0.191943
$297$	2.39041	0.138706
$298$	26.6416	1.54331
$299$	0	0
$300$	−68.0245	−3.92739
$301$	8.55596	0.493157
$302$	10.3796	0.597277
$303$	−7.96343	−0.457487
$304$	5.33285	0.305860
$305$	12.1854	0.697736
$306$	25.3499	1.44916
$307$	−0.232419	−0.0132649	−0.00663244	−	0.999978i	$-0.502111\pi$
$307$	−0.232419	−0.0132649	−0.00663244	+	0.999978i	$0.502111\pi$
$308$	6.43772	0.366823
$309$	18.0561	1.02718
$310$	46.5298	2.64271
$311$	14.5723	0.826320	0.413160	−	0.910658i	$-0.364425\pi$
$311$	14.5723	0.826320	0.413160	+	0.910658i	$0.364425\pi$
$312$	3.95490	0.223902
$313$	3.14964	0.178028	0.0890140	−	0.996030i	$-0.471628\pi$
$313$	3.14964	0.178028	0.0890140	+	0.996030i	$0.471628\pi$
$314$	−26.6297	−1.50280
$315$	−24.0689	−1.35613
$316$	19.4838	1.09605
$317$	−16.7399	−0.940209	−0.470105	−	0.882611i	$-0.655784\pi$
$317$	−16.7399	−0.940209	−0.470105	+	0.882611i	$0.655784\pi$
$318$	6.62952	0.371765
$319$	1.72451	0.0965541
$320$	42.0397	2.35009
$321$	6.11646	0.341388
$322$	0	0
$323$	9.79010	0.544736
$324$	−24.6621	−1.37012
$325$	52.4394	2.90881
$326$	34.3065	1.90006
$327$	21.5652	1.19256
$328$	−1.14784	−0.0633789
$329$	20.1908	1.11316
$330$	−19.7607	−1.08779
$331$	−14.9545	−0.821972	−0.410986	−	0.911642i	$-0.634815\pi$
$331$	−14.9545	−0.821972	−0.410986	+	0.911642i	$0.634815\pi$
$332$	−2.00878	−0.110246
$333$	13.5702	0.743645
$334$	13.9726	0.764546
$335$	−23.2312	−1.26926
$336$	22.3983	1.22193
$337$	−32.5164	−1.77128	−0.885641	−	0.464370i	$-0.846281\pi$
$337$	−32.5164	−1.77128	−0.885641	+	0.464370i	$0.846281\pi$
$338$	−3.11623	−0.169500
$339$	25.0738	1.36182
$340$	61.8771	3.35576
$341$	5.22427	0.282910
$342$	6.03504	0.326337
$343$	−16.3219	−0.881301
$344$	−1.38511	−0.0746803
$345$	0	0
$346$	−25.6568	−1.37932
$347$	20.6269	1.10731	0.553656	−	0.832746i	$-0.313232\pi$
$347$	20.6269	1.10731	0.553656	+	0.832746i	$0.313232\pi$
$348$	−8.52297	−0.456879
$349$	−12.4441	−0.666117	−0.333058	−	0.942906i	$-0.608081\pi$
$349$	−12.4441	−0.666117	−0.333058	+	0.942906i	$0.608081\pi$
$350$	−81.7879	−4.37175
$351$	9.10732	0.486113
$352$	8.11794	0.432688
$353$	−10.9466	−0.582631	−0.291316	−	0.956627i	$-0.594093\pi$
$353$	−10.9466	−0.582631	−0.291316	+	0.956627i	$0.594093\pi$
$354$	63.1312	3.35539
$355$	−2.86013	−0.151800
$356$	−7.53512	−0.399361
$357$	41.1191	2.17625
$358$	−34.0087	−1.79742
$359$	23.7664	1.25434	0.627172	−	0.778881i	$-0.284212\pi$
$359$	23.7664	1.25434	0.627172	+	0.778881i	$0.284212\pi$
$360$	3.89647	0.205362
$361$	−16.6693	−0.877330
$362$	−36.9168	−1.94030
$363$	−2.21869	−0.116451
$364$	24.5273	1.28558
$365$	−48.6700	−2.54750
$366$	−12.8328	−0.670782
$367$	−15.9940	−0.834881	−0.417441	−	0.908704i	$-0.637073\pi$
$367$	−15.9940	−0.834881	−0.417441	+	0.908704i	$0.637073\pi$
$368$	0	0
$369$	4.71684	0.245549
$370$	62.8642	3.26815
$371$	4.19996	0.218051
$372$	−25.8196	−1.33869
$373$	−33.4633	−1.73267	−0.866333	−	0.499467i	$-0.833529\pi$
$373$	−33.4633	−1.73267	−0.866333	+	0.499467i	$0.833529\pi$
$374$	13.1852	0.681789
$375$	84.2275	4.34949
$376$	−3.26867	−0.168569
$377$	6.57028	0.338386
$378$	−14.2044	−0.730594
$379$	−17.3556	−0.891496	−0.445748	−	0.895159i	$-0.647062\pi$
$379$	−17.3556	−0.891496	−0.445748	+	0.895159i	$0.647062\pi$
$380$	14.7311	0.755688
$381$	32.0203	1.64045
$382$	−4.67453	−0.239170
$383$	27.8536	1.42326	0.711628	−	0.702557i	$-0.247958\pi$
$383$	27.8536	1.42326	0.711628	+	0.702557i	$0.247958\pi$
$384$	−8.25065	−0.421039
$385$	−12.5189	−0.638022
$386$	43.4431	2.21119
$387$	5.69185	0.289333
$388$	5.92111	0.300599
$389$	−9.32078	−0.472583	−0.236291	−	0.971682i	$-0.575932\pi$
$389$	−9.32078	−0.472583	−0.236291	+	0.971682i	$0.575932\pi$
$390$	−75.2871	−3.81231
$391$	0	0
$392$	−0.632724	−0.0319574
$393$	−16.4593	−0.830262
$394$	24.0789	1.21308
$395$	−37.8884	−1.90637
$396$	4.28270	0.215214
$397$	−11.3041	−0.567337	−0.283669	−	0.958922i	$-0.591552\pi$
$397$	−11.3041	−0.567337	−0.283669	+	0.958922i	$0.591552\pi$
$398$	−41.5243	−2.08142
$399$	9.78921	0.490074
$400$	−48.0788	−2.40394
$401$	−8.03359	−0.401179	−0.200589	−	0.979675i	$-0.564286\pi$
$401$	−8.03359	−0.401179	−0.200589	+	0.979675i	$0.564286\pi$
$402$	24.4654	1.22023
$403$	19.9041	0.991495
$404$	7.99522	0.397777
$405$	47.9583	2.38307
$406$	−10.2474	−0.508572
$407$	7.05826	0.349865
$408$	−6.65671	−0.329556
$409$	33.7950	1.67106	0.835528	−	0.549448i	$-0.185162\pi$
$409$	33.7950	1.67106	0.835528	+	0.549448i	$0.185162\pi$
$410$	21.8508	1.07913
$411$	−9.80250	−0.483521
$412$	−18.1282	−0.893112
$413$	39.9951	1.96803
$414$	0	0
$415$	3.90630	0.191753
$416$	30.9288	1.51641
$417$	0.798363	0.0390960
$418$	3.13899	0.153533
$419$	26.9868	1.31839	0.659195	−	0.751972i	$-0.270897\pi$
$419$	26.9868	1.31839	0.659195	+	0.751972i	$0.270897\pi$
$420$	61.8715	3.01902
$421$	−10.9779	−0.535030	−0.267515	−	0.963554i	$-0.586203\pi$
$421$	−10.9779	−0.535030	−0.267515	+	0.963554i	$0.586203\pi$
$422$	−35.8737	−1.74631
$423$	13.4320	0.653085
$424$	−0.679925	−0.0330201
$425$	−88.2636	−4.28141
$426$	3.01208	0.145936
$427$	−8.12990	−0.393433
$428$	−6.14087	−0.296830
$429$	−8.45308	−0.408119
$430$	26.3675	1.27156
$431$	−16.4497	−0.792356	−0.396178	−	0.918174i	$-0.629664\pi$
$431$	−16.4497	−0.792356	−0.396178	+	0.918174i	$0.629664\pi$
$432$	−8.35000	−0.401740
$433$	27.9939	1.34530	0.672651	−	0.739960i	$-0.265156\pi$
$433$	27.9939	1.34530	0.672651	+	0.739960i	$0.265156\pi$
$434$	−31.0438	−1.49015
$435$	16.5739	0.794658
$436$	−21.6513	−1.03691
$437$	0	0
$438$	51.2556	2.44909
$439$	33.7378	1.61022	0.805109	−	0.593126i	$-0.202107\pi$
$439$	33.7378	1.61022	0.805109	+	0.593126i	$0.202107\pi$
$440$	2.02667	0.0966175
$441$	2.60006	0.123812
$442$	50.2347	2.38942
$443$	−25.3926	−1.20644	−0.603218	−	0.797576i	$-0.706115\pi$
$443$	−25.3926	−1.20644	−0.603218	+	0.797576i	$0.706115\pi$
$444$	−34.8837	−1.65551
$445$	14.6529	0.694615
$446$	23.2164	1.09933
$447$	28.7484	1.35975
$448$	−28.0481	−1.32515
$449$	−14.1215	−0.666435	−0.333218	−	0.942850i	$-0.608134\pi$
$449$	−14.1215	−0.666435	−0.333218	+	0.942850i	$0.608134\pi$
$450$	−54.4094	−2.56489
$451$	2.45336	0.115524
$452$	−25.1739	−1.18408
$453$	11.2004	0.526239
$454$	−21.0478	−0.987821
$455$	−47.6961	−2.23603
$456$	−1.58476	−0.0742133
$457$	−17.6303	−0.824710	−0.412355	−	0.911023i	$-0.635294\pi$
$457$	−17.6303	−0.824710	−0.412355	+	0.911023i	$0.635294\pi$
$458$	9.16170	0.428098
$459$	−15.3290	−0.715497
$460$	0	0
$461$	17.8012	0.829084	0.414542	−	0.910030i	$-0.363942\pi$
$461$	17.8012	0.829084	0.414542	+	0.910030i	$0.363942\pi$
$462$	13.1840	0.613374
$463$	−7.20653	−0.334916	−0.167458	−	0.985879i	$-0.553556\pi$
$463$	−7.20653	−0.334916	−0.167458	+	0.985879i	$0.553556\pi$
$464$	−6.02393	−0.279654
$465$	50.2093	2.32840
$466$	23.3520	1.08176
$467$	−3.32989	−0.154089	−0.0770445	−	0.997028i	$-0.524548\pi$
$467$	−3.32989	−0.154089	−0.0770445	+	0.997028i	$0.524548\pi$
$468$	16.3168	0.754244
$469$	15.4994	0.715698
$470$	62.2236	2.87016
$471$	−28.7355	−1.32406
$472$	−6.47476	−0.298025
$473$	2.96049	0.136124
$474$	39.9013	1.83273
$475$	−21.0129	−0.964138
$476$	−41.2832	−1.89221
$477$	2.79402	0.127930
$478$	−32.5033	−1.48667
$479$	−18.9619	−0.866390	−0.433195	−	0.901300i	$-0.642614\pi$
$479$	−18.9619	−0.866390	−0.433195	+	0.901300i	$0.642614\pi$
$480$	78.0197	3.56110
$481$	26.8915	1.22615
$482$	6.15944	0.280555
$483$	0	0
$484$	2.22755	0.101252
$485$	−11.5143	−0.522837
$486$	−35.7614	−1.62217
$487$	−43.1625	−1.95588	−0.977940	−	0.208885i	$-0.933017\pi$
$487$	−43.1625	−1.95588	−0.977940	+	0.208885i	$0.933017\pi$
$488$	1.31614	0.0595787
$489$	37.0194	1.67408
$490$	12.0448	0.544128
$491$	−19.9626	−0.900898	−0.450449	−	0.892802i	$-0.648736\pi$
$491$	−19.9626	−0.900898	−0.450449	+	0.892802i	$0.648736\pi$
$492$	−12.1251	−0.546642
$493$	−11.0588	−0.498063
$494$	11.9594	0.538077
$495$	−8.32819	−0.374324
$496$	−18.2490	−0.819404
$497$	1.90822	0.0855954
$498$	−4.11383	−0.184345
$499$	6.06017	0.271291	0.135645	−	0.990757i	$-0.456689\pi$
$499$	6.06017	0.271291	0.135645	+	0.990757i	$0.456689\pi$
$500$	−84.5637	−3.78180
$501$	15.0775	0.673614
$502$	8.30080	0.370483
$503$	−40.6847	−1.81404	−0.907020	−	0.421089i	$-0.861648\pi$
$503$	−40.6847	−1.81404	−0.907020	+	0.421089i	$0.861648\pi$
$504$	−2.59965	−0.115798
$505$	−15.5476	−0.691860
$506$	0	0
$507$	−3.36266	−0.149341
$508$	−32.1481	−1.42634
$509$	35.2348	1.56175	0.780877	−	0.624685i	$-0.214773\pi$
$509$	35.2348	1.56175	0.780877	+	0.624685i	$0.214773\pi$
$510$	126.720	5.61125
$511$	32.4717	1.43646
$512$	−31.6256	−1.39767
$513$	−3.64938	−0.161124
$514$	10.1961	0.449732
$515$	35.2524	1.55341
$516$	−14.6315	−0.644116
$517$	6.98634	0.307259
$518$	−41.9418	−1.84282
$519$	−27.6857	−1.21527
$520$	7.72146	0.338609
$521$	18.3373	0.803370	0.401685	−	0.915778i	$-0.368425\pi$
$521$	18.3373	0.803370	0.401685	+	0.915778i	$0.368425\pi$
$522$	−6.81711	−0.298377
$523$	2.80993	0.122870	0.0614348	−	0.998111i	$-0.480432\pi$
$523$	2.80993	0.122870	0.0614348	+	0.998111i	$0.480432\pi$
$524$	16.5250	0.721898
$525$	−88.2556	−3.85179
$526$	−21.3570	−0.931208
$527$	−33.5017	−1.45936
$528$	7.75017	0.337283
$529$	0	0
$530$	12.9433	0.562222
$531$	26.6068	1.15464
$532$	−9.82829	−0.426110
$533$	9.34713	0.404869
$534$	−15.4314	−0.667781
$535$	11.9416	0.516282
$536$	−2.50918	−0.108380
$537$	−36.6980	−1.58364
$538$	50.7207	2.18672
$539$	1.35236	0.0582504
$540$	−23.0654	−0.992578
$541$	35.7209	1.53576	0.767881	−	0.640592i	$-0.221311\pi$
$541$	35.7209	1.53576	0.767881	+	0.640592i	$0.221311\pi$
$542$	−21.3920	−0.918865
$543$	−39.8361	−1.70953
$544$	−52.0580	−2.23197
$545$	42.1034	1.80351
$546$	50.2301	2.14965
$547$	28.2178	1.20651	0.603253	−	0.797550i	$-0.293871\pi$
$547$	28.2178	1.20651	0.603253	+	0.797550i	$0.293871\pi$
$548$	9.84162	0.420413
$549$	−5.40842	−0.230826
$550$	−28.2999	−1.20671
$551$	−2.63276	−0.112159
$552$	0	0
$553$	25.2784	1.07495
$554$	−28.4039	−1.20677
$555$	67.8354	2.87945
$556$	−0.801550	−0.0339933
$557$	18.2657	0.773945	0.386972	−	0.922091i	$-0.373521\pi$
$557$	18.2657	0.773945	0.386972	+	0.922091i	$0.373521\pi$
$558$	−20.6519	−0.874264
$559$	11.2793	0.477063
$560$	43.7300	1.84793
$561$	14.2278	0.600700
$562$	36.8652	1.55507
$563$	−0.631160	−0.0266002	−0.0133001	−	0.999912i	$-0.504234\pi$
$563$	−0.631160	−0.0266002	−0.0133001	+	0.999912i	$0.504234\pi$
$564$	−34.5283	−1.45390
$565$	48.9535	2.05949
$566$	−49.0772	−2.06287
$567$	−31.9969	−1.34374
$568$	−0.308919	−0.0129620
$569$	−14.4853	−0.607256	−0.303628	−	0.952791i	$-0.598198\pi$
$569$	−14.4853	−0.607256	−0.303628	+	0.952791i	$0.598198\pi$
$570$	30.1681	1.26360
$571$	11.2868	0.472339	0.236169	−	0.971712i	$-0.424108\pi$
$571$	11.2868	0.472339	0.236169	+	0.971712i	$0.424108\pi$
$572$	8.48682	0.354852
$573$	−5.04418	−0.210724
$574$	−14.5784	−0.608491
$575$	0	0
$576$	−18.6590	−0.777458
$577$	4.89983	0.203983	0.101991	−	0.994785i	$-0.467479\pi$
$577$	4.89983	0.203983	0.101991	+	0.994785i	$0.467479\pi$
$578$	−49.5990	−2.06305
$579$	46.8785	1.94820
$580$	−16.6401	−0.690940
$581$	−2.60621	−0.108124
$582$	12.1260	0.502639
$583$	1.45325	0.0601874
$584$	−5.25679	−0.217528
$585$	−31.7299	−1.31187
$586$	−67.1125	−2.77239
$587$	9.93826	0.410196	0.205098	−	0.978741i	$-0.434249\pi$
$587$	9.93826	0.410196	0.205098	+	0.978741i	$0.434249\pi$
$588$	−6.68372	−0.275632
$589$	−7.97574	−0.328635
$590$	123.256	5.07437
$591$	25.9830	1.06880
$592$	−24.6554	−1.01333
$593$	9.48537	0.389517	0.194759	−	0.980851i	$-0.437608\pi$
$593$	9.48537	0.389517	0.194759	+	0.980851i	$0.437608\pi$
$594$	−4.91493	−0.201662
$595$	80.2800	3.29116
$596$	−28.8631	−1.18228
$597$	−44.8079	−1.83387
$598$	0	0
$599$	15.1557	0.619247	0.309623	−	0.950859i	$-0.399797\pi$
$599$	15.1557	0.619247	0.309623	+	0.950859i	$0.399797\pi$
$600$	14.2876	0.583288
$601$	−22.0796	−0.900645	−0.450323	−	0.892866i	$-0.648691\pi$
$601$	−22.0796	−0.900645	−0.450323	+	0.892866i	$0.648691\pi$
$602$	−17.5919	−0.716993
$603$	10.3110	0.419897
$604$	−11.2451	−0.457556
$605$	−4.33173	−0.176110
$606$	16.3736	0.665133
$607$	−31.3695	−1.27325	−0.636624	−	0.771174i	$-0.719670\pi$
$607$	−31.3695	−1.27325	−0.636624	+	0.771174i	$0.719670\pi$
$608$	−12.3934	−0.502620
$609$	−11.0578	−0.448084
$610$	−25.0545	−1.01443
$611$	26.6175	1.07683
$612$	−27.4637	−1.11015
$613$	−21.6870	−0.875929	−0.437965	−	0.898992i	$-0.644300\pi$
$613$	−21.6870	−0.875929	−0.437965	+	0.898992i	$0.644300\pi$
$614$	0.477878	0.0192856
$615$	23.5787	0.950784
$616$	−1.35215	−0.0544798
$617$	48.9622	1.97114	0.985572	−	0.169257i	$-0.0541367\pi$
$617$	48.9622	1.97114	0.985572	+	0.169257i	$0.0541367\pi$
$618$	−37.1252	−1.49340
$619$	35.5606	1.42930	0.714651	−	0.699481i	$-0.246585\pi$
$619$	35.5606	1.42930	0.714651	+	0.699481i	$0.246585\pi$
$620$	−50.4097	−2.02450
$621$	0	0
$622$	−29.9621	−1.20137
$623$	−9.77614	−0.391673
$624$	29.5276	1.18205
$625$	95.6245	3.82498
$626$	−6.47597	−0.258832
$627$	3.38722	0.135272
$628$	28.8502	1.15125
$629$	−45.2626	−1.80474
$630$	49.4880	1.97165
$631$	24.3548	0.969549	0.484775	−	0.874639i	$-0.338902\pi$
$631$	24.3548	0.969549	0.484775	+	0.874639i	$0.338902\pi$
$632$	−4.09229	−0.162783
$633$	−38.7106	−1.53861
$634$	34.4190	1.36695
$635$	62.5157	2.48086
$636$	−7.18232	−0.284798
$637$	5.15242	0.204146
$638$	−3.54577	−0.140378
$639$	1.26944	0.0502185
$640$	−16.1084	−0.636740
$641$	−8.93168	−0.352780	−0.176390	−	0.984320i	$-0.556442\pi$
$641$	−8.93168	−0.352780	−0.176390	+	0.984320i	$0.556442\pi$
$642$	−12.5761	−0.496337
$643$	−21.7066	−0.856024	−0.428012	−	0.903773i	$-0.640786\pi$
$643$	−21.7066	−0.856024	−0.428012	+	0.903773i	$0.640786\pi$
$644$	0	0
$645$	28.4526	1.12032
$646$	−20.1294	−0.791982
$647$	20.5879	0.809392	0.404696	−	0.914451i	$-0.367377\pi$
$647$	20.5879	0.809392	0.404696	+	0.914451i	$0.367377\pi$
$648$	5.17993	0.203487
$649$	13.8389	0.543226
$650$	−107.821	−4.22907
$651$	−33.4987	−1.31292
$652$	−37.1672	−1.45558
$653$	41.9239	1.64061	0.820305	−	0.571927i	$-0.193804\pi$
$653$	41.9239	1.64061	0.820305	+	0.571927i	$0.193804\pi$
$654$	−44.3402	−1.73384
$655$	−32.1348	−1.25561
$656$	−8.56988	−0.334598
$657$	21.6018	0.842766
$658$	−41.5144	−1.61840
$659$	13.8062	0.537812	0.268906	−	0.963166i	$-0.413338\pi$
$659$	13.8062	0.537812	0.268906	+	0.963166i	$0.413338\pi$
$660$	21.4085	0.833324
$661$	0.0154939	0.000602642 0	0.000301321	−	1.00000i	$-0.499904\pi$
$661$	0.0154939	0.000602642 0	0.000301321		1.00000i	$0.499904\pi$
$662$	30.7479	1.19505
$663$	54.2071	2.10523
$664$	0.421915	0.0163735
$665$	19.1122	0.741141
$666$	−27.9018	−1.08117
$667$	0	0
$668$	−15.1377	−0.585695
$669$	25.0523	0.968578
$670$	47.7658	1.84535
$671$	−2.81307	−0.108597
$672$	−52.0533	−2.00800
$673$	45.0944	1.73826	0.869131	−	0.494581i	$-0.164679\pi$
$673$	45.0944	1.73826	0.869131	+	0.494581i	$0.164679\pi$
$674$	66.8570	2.57524
$675$	32.9013	1.26637
$676$	3.37608	0.129849
$677$	−24.0327	−0.923653	−0.461827	−	0.886970i	$-0.652806\pi$
$677$	−24.0327	−0.923653	−0.461827	+	0.886970i	$0.652806\pi$
$678$	−51.5543	−1.97993
$679$	7.68211	0.294812
$680$	−12.9964	−0.498390
$681$	−22.7122	−0.870333
$682$	−10.7416	−0.411318
$683$	10.3994	0.397920	0.198960	−	0.980008i	$-0.436244\pi$
$683$	10.3994	0.397920	0.198960	+	0.980008i	$0.436244\pi$
$684$	−6.53827	−0.249997
$685$	−19.1382	−0.731232
$686$	33.5595	1.28131
$687$	9.88619	0.377182
$688$	−10.3414	−0.394261
$689$	5.53678	0.210935
$690$	0	0
$691$	14.8474	0.564820	0.282410	−	0.959294i	$-0.408866\pi$
$691$	14.8474	0.564820	0.282410	+	0.959294i	$0.408866\pi$
$692$	27.7962	1.05665
$693$	5.55641	0.211071
$694$	−42.4110	−1.60990
$695$	1.55871	0.0591251
$696$	1.79013	0.0678547
$697$	−15.7327	−0.595917
$698$	25.5863	0.968456
$699$	25.1987	0.953101
$700$	88.6079	3.34906
$701$	5.40765	0.204244	0.102122	−	0.994772i	$-0.467437\pi$
$701$	5.40765	0.204244	0.102122	+	0.994772i	$0.467437\pi$
$702$	−18.7256	−0.706751
$703$	−10.7756	−0.406411
$704$	−9.70506	−0.365773
$705$	67.1442	2.52880
$706$	22.5074	0.847077
$707$	10.3731	0.390120
$708$	−68.3955	−2.57046
$709$	5.20178	0.195357	0.0976785	−	0.995218i	$-0.468858\pi$
$709$	5.20178	0.195357	0.0976785	+	0.995218i	$0.468858\pi$
$710$	5.88071	0.220699
$711$	16.8165	0.630667
$712$	1.58265	0.0593122
$713$	0	0
$714$	−84.5450	−3.16402
$715$	−16.5036	−0.617199
$716$	36.8445	1.37694
$717$	−35.0737	−1.30985
$718$	−48.8661	−1.82367
$719$	25.9654	0.968346	0.484173	−	0.874972i	$-0.339121\pi$
$719$	25.9654	0.968346	0.484173	+	0.874972i	$0.339121\pi$
$720$	29.0914	1.08417
$721$	−23.5197	−0.875920
$722$	34.2737	1.27554
$723$	6.64652	0.247187
$724$	39.9951	1.48641
$725$	23.7359	0.881530
$726$	4.56186	0.169306
$727$	28.3183	1.05027	0.525133	−	0.851020i	$-0.324015\pi$
$727$	28.3183	1.05027	0.525133	+	0.851020i	$0.324015\pi$
$728$	−5.15161	−0.190931
$729$	−5.37514	−0.199079
$730$	100.070	3.70377
$731$	−18.9848	−0.702177
$732$	13.9029	0.513866
$733$	−47.7054	−1.76204	−0.881019	−	0.473081i	$-0.843142\pi$
$733$	−47.7054	−1.76204	−0.881019	+	0.473081i	$0.843142\pi$
$734$	32.8853	1.21382
$735$	12.9973	0.479411
$736$	0	0
$737$	5.36304	0.197550
$738$	−9.69829	−0.356999
$739$	7.71007	0.283619	0.141810	−	0.989894i	$-0.454708\pi$
$739$	7.71007	0.283619	0.141810	+	0.989894i	$0.454708\pi$
$740$	−68.1061	−2.50363
$741$	12.9051	0.474080
$742$	−8.63553	−0.317020
$743$	−25.7124	−0.943295	−0.471648	−	0.881787i	$-0.656341\pi$
$743$	−25.7124	−0.943295	−0.471648	+	0.881787i	$0.656341\pi$
$744$	5.42305	0.198819
$745$	56.1277	2.05636
$746$	68.8040	2.51909
$747$	−1.73378	−0.0634357
$748$	−14.2846	−0.522298
$749$	−7.96723	−0.291116
$750$	−173.180	−6.32365
$751$	−10.9593	−0.399911	−0.199955	−	0.979805i	$-0.564080\pi$
$751$	−10.9593	−0.399911	−0.199955	+	0.979805i	$0.564080\pi$
$752$	−24.4041	−0.889927
$753$	8.95722	0.326419
$754$	−13.5091	−0.491974
$755$	21.8673	0.795834
$756$	15.3888	0.559686
$757$	43.3639	1.57609	0.788044	−	0.615619i	$-0.211094\pi$
$757$	43.3639	1.57609	0.788044	+	0.615619i	$0.211094\pi$
$758$	35.6848	1.29613
$759$	0	0
$760$	−3.09405	−0.112233
$761$	−27.2775	−0.988807	−0.494404	−	0.869233i	$-0.664613\pi$
$761$	−27.2775	−0.988807	−0.494404	+	0.869233i	$0.664613\pi$
$762$	−65.8370	−2.38502
$763$	−28.0906	−1.01695
$764$	5.06431	0.183220
$765$	53.4063	1.93091
$766$	−57.2699	−2.06925
$767$	52.7254	1.90380
$768$	−26.1009	−0.941837
$769$	−52.6492	−1.89858	−0.949290	−	0.314402i	$-0.898196\pi$
$769$	−52.6492	−1.89858	−0.949290	+	0.314402i	$0.898196\pi$
$770$	25.7401	0.927609
$771$	11.0024	0.396242
$772$	−47.0656	−1.69393
$773$	−28.8150	−1.03640	−0.518202	−	0.855258i	$-0.673398\pi$
$773$	−28.8150	−1.03640	−0.518202	+	0.855258i	$0.673398\pi$
$774$	−11.7030	−0.420657
$775$	71.9061	2.58294
$776$	−1.24365	−0.0446443
$777$	−45.2585	−1.62364
$778$	19.1645	0.687080
$779$	−3.74547	−0.134195
$780$	81.5649	2.92049
$781$	0.660274	0.0236265
$782$	0	0
$783$	4.12229	0.147319
$784$	−4.72397	−0.168713
$785$	−56.1026	−2.00239
$786$	33.8420	1.20710
$787$	12.3824	0.441384	0.220692	−	0.975344i	$-0.429168\pi$
$787$	12.3824	0.441384	0.220692	+	0.975344i	$0.429168\pi$
$788$	−26.0867	−0.929301
$789$	−23.0458	−0.820454
$790$	77.9024	2.77164
$791$	−32.6609	−1.16129
$792$	−0.899520	−0.0319630
$793$	−10.7176	−0.380593
$794$	23.2424	0.824842
$795$	13.9669	0.495353
$796$	44.9868	1.59451
$797$	2.11487	0.0749126	0.0374563	−	0.999298i	$-0.488075\pi$
$797$	2.11487	0.0749126	0.0374563	+	0.999298i	$0.488075\pi$
$798$	−20.1276	−0.712510
$799$	−44.8014	−1.58496
$800$	111.734	3.95040
$801$	−6.50358	−0.229793
$802$	16.5179	0.583267
$803$	11.2357	0.396499
$804$	−26.5055	−0.934777
$805$	0	0
$806$	−40.9249	−1.44152
$807$	54.7316	1.92664
$808$	−1.67928	−0.0590770
$809$	32.6545	1.14807	0.574036	−	0.818830i	$-0.305377\pi$
$809$	32.6545	1.14807	0.574036	+	0.818830i	$0.305377\pi$
$810$	−98.6071	−3.46470
$811$	26.1035	0.916619	0.458309	−	0.888793i	$-0.348455\pi$
$811$	26.1035	0.916619	0.458309	+	0.888793i	$0.348455\pi$
$812$	11.1019	0.389601
$813$	−23.0836	−0.809579
$814$	−14.5125	−0.508663
$815$	72.2759	2.53171
$816$	−49.6996	−1.73983
$817$	−4.51970	−0.158124
$818$	−69.4860	−2.42952
$819$	21.1696	0.739725
$820$	−23.6728	−0.826690
$821$	−21.6788	−0.756595	−0.378297	−	0.925684i	$-0.623490\pi$
$821$	−21.6788	−0.756595	−0.378297	+	0.925684i	$0.623490\pi$
$822$	20.1549	0.702984
$823$	17.4941	0.609805	0.304903	−	0.952384i	$-0.401376\pi$
$823$	17.4941	0.609805	0.304903	+	0.952384i	$0.401376\pi$
$824$	3.80757	0.132643
$825$	−30.5378	−1.06319
$826$	−82.2340	−2.86129
$827$	6.05049	0.210396	0.105198	−	0.994451i	$-0.466452\pi$
$827$	6.05049	0.210396	0.105198	+	0.994451i	$0.466452\pi$
$828$	0	0
$829$	37.6759	1.30854	0.654269	−	0.756262i	$-0.272976\pi$
$829$	37.6759	1.30854	0.654269	+	0.756262i	$0.272976\pi$
$830$	−8.03174	−0.278786
$831$	−30.6500	−1.06324
$832$	−36.9756	−1.28190
$833$	−8.67232	−0.300478
$834$	−1.64152	−0.0568410
$835$	29.4370	1.01871
$836$	−3.40074	−0.117617
$837$	12.4882	0.431654
$838$	−55.4875	−1.91678
$839$	−10.2034	−0.352262	−0.176131	−	0.984367i	$-0.556358\pi$
$839$	−10.2034	−0.352262	−0.176131	+	0.984367i	$0.556358\pi$
$840$	−12.9952	−0.448378
$841$	−26.0261	−0.897450
$842$	22.5717	0.777871
$843$	39.7805	1.37011
$844$	38.8651	1.33779
$845$	−6.56517	−0.225849
$846$	−27.6175	−0.949508
$847$	2.89005	0.0993031
$848$	−5.07638	−0.174323
$849$	−52.9582	−1.81752
$850$	181.479	6.22467
$851$	0	0
$852$	−3.26324	−0.111797
$853$	−46.9586	−1.60783	−0.803916	−	0.594743i	$-0.797254\pi$
$853$	−46.9586	−1.60783	−0.803916	+	0.594743i	$0.797254\pi$
$854$	16.7159	0.572006
$855$	12.7144	0.434824
$856$	1.28980	0.0440846
$857$	−24.1920	−0.826383	−0.413192	−	0.910644i	$-0.635586\pi$
$857$	−24.1920	−0.826383	−0.413192	+	0.910644i	$0.635586\pi$
$858$	17.3804	0.593356
$859$	−15.6270	−0.533188	−0.266594	−	0.963809i	$-0.585898\pi$
$859$	−15.6270	−0.533188	−0.266594	+	0.963809i	$0.585898\pi$
$860$	−28.5662	−0.974100
$861$	−15.7312	−0.536119
$862$	33.8223	1.15199
$863$	−44.1104	−1.50154	−0.750769	−	0.660565i	$-0.770317\pi$
$863$	−44.1104	−1.50154	−0.750769	+	0.660565i	$0.770317\pi$
$864$	19.4052	0.660179
$865$	−54.0529	−1.83785
$866$	−57.5583	−1.95591
$867$	−53.5212	−1.81767
$868$	33.6324	1.14156
$869$	8.74672	0.296712
$870$	−34.0776	−1.15534
$871$	20.4328	0.692340
$872$	4.54755	0.153999
$873$	5.11053	0.172965
$874$	0	0
$875$	−109.714	−3.70900
$876$	−55.5296	−1.87617
$877$	6.30847	0.213022	0.106511	−	0.994312i	$-0.466032\pi$
$877$	6.30847	0.213022	0.106511	+	0.994312i	$0.466032\pi$
$878$	−69.3684	−2.34107
$879$	−72.4197	−2.44266
$880$	15.1312	0.510074
$881$	5.76879	0.194355	0.0971777	−	0.995267i	$-0.469018\pi$
$881$	5.76879	0.194355	0.0971777	+	0.995267i	$0.469018\pi$
$882$	−5.34598	−0.180009
$883$	5.02373	0.169062	0.0845310	−	0.996421i	$-0.473061\pi$
$883$	5.02373	0.169062	0.0845310	+	0.996421i	$0.473061\pi$
$884$	−54.4235	−1.83046
$885$	133.003	4.47084
$886$	52.2097	1.75402
$887$	11.8215	0.396926	0.198463	−	0.980108i	$-0.436405\pi$
$887$	11.8215	0.396926	0.198463	+	0.980108i	$0.436405\pi$
$888$	7.32683	0.245872
$889$	−41.7093	−1.39889
$890$	−30.1279	−1.00989
$891$	−11.0714	−0.370906
$892$	−25.1523	−0.842161
$893$	−10.6659	−0.356919
$894$	−59.1096	−1.97692
$895$	−71.6484	−2.39494
$896$	10.7472	0.359039
$897$	0	0
$898$	29.0352	0.968918
$899$	9.00931	0.300477
$900$	58.9464	1.96488
$901$	−9.31926	−0.310470
$902$	−5.04435	−0.167959
$903$	−18.9831	−0.631717
$904$	5.28742	0.175857
$905$	−77.7751	−2.58533
$906$	−23.0291	−0.765090
$907$	−7.56238	−0.251105	−0.125552	−	0.992087i	$-0.540070\pi$
$907$	−7.56238	−0.251105	−0.125552	+	0.992087i	$0.540070\pi$
$908$	22.8028	0.756739
$909$	6.90069	0.228881
$910$	98.0681	3.25093
$911$	21.5290	0.713289	0.356644	−	0.934240i	$-0.383921\pi$
$911$	21.5290	0.713289	0.356644	+	0.934240i	$0.383921\pi$
$912$	−11.8320	−0.391795
$913$	−0.901787	−0.0298448
$914$	36.2497	1.19903
$915$	−27.0358	−0.893775
$916$	−9.92565	−0.327953
$917$	21.4397	0.708001
$918$	31.5180	1.04025
$919$	−24.9287	−0.822323	−0.411161	−	0.911563i	$-0.634877\pi$
$919$	−24.9287	−0.822323	−0.411161	+	0.911563i	$0.634877\pi$
$920$	0	0
$921$	0.515668	0.0169918
$922$	−36.6010	−1.20539
$923$	2.51560	0.0828020
$924$	−14.2833	−0.469887
$925$	97.1489	3.19424
$926$	14.8173	0.486928
$927$	−15.6465	−0.513898
$928$	13.9995	0.459555
$929$	15.0679	0.494362	0.247181	−	0.968969i	$-0.420496\pi$
$929$	15.0679	0.494362	0.247181	+	0.968969i	$0.420496\pi$
$930$	−103.235	−3.38522
$931$	−2.06462	−0.0676651
$932$	−25.2992	−0.828704
$933$	−32.3315	−1.05849
$934$	6.84659	0.224027
$935$	27.7781	0.908441
$936$	−3.42711	−0.112019
$937$	19.9596	0.652053	0.326026	−	0.945361i	$-0.394290\pi$
$937$	19.9596	0.652053	0.326026	+	0.945361i	$0.394290\pi$
$938$	−31.8684	−1.04054
$939$	−6.98808	−0.228047
$940$	−67.4122	−2.19874
$941$	46.8612	1.52763	0.763816	−	0.645434i	$-0.223323\pi$
$941$	46.8612	1.52763	0.763816	+	0.645434i	$0.223323\pi$
$942$	59.0832	1.92503
$943$	0	0
$944$	−48.3411	−1.57337
$945$	−29.9253	−0.973471
$946$	−6.08707	−0.197908
$947$	29.1621	0.947641	0.473820	−	0.880622i	$-0.342875\pi$
$947$	29.1621	0.947641	0.473820	+	0.880622i	$0.342875\pi$
$948$	−43.2285	−1.40400
$949$	42.8073	1.38958
$950$	43.2046	1.40174
$951$	37.1408	1.20437
$952$	8.67096	0.281027
$953$	16.2262	0.525619	0.262810	−	0.964848i	$-0.415351\pi$
$953$	16.2262	0.525619	0.262810	+	0.964848i	$0.415351\pi$
$954$	−5.74479	−0.185994
$955$	−9.84814	−0.318678
$956$	35.2137	1.13889
$957$	−3.82616	−0.123682
$958$	38.9875	1.25963
$959$	12.7686	0.412320
$960$	−93.2732	−3.01038
$961$	−3.70703	−0.119582
$962$	−55.2917	−1.78267
$963$	−5.30020	−0.170797
$964$	−6.67305	−0.214924
$965$	91.5245	2.94628
$966$	0	0
$967$	24.8078	0.797764	0.398882	−	0.917002i	$-0.369398\pi$
$967$	24.8078	0.797764	0.398882	+	0.917002i	$0.369398\pi$
$968$	−0.467865	−0.0150378
$969$	−21.7212	−0.697787
$970$	23.6745	0.760143
$971$	−31.7098	−1.01761	−0.508807	−	0.860880i	$-0.669913\pi$
$971$	−31.7098	−1.01761	−0.508807	+	0.860880i	$0.669913\pi$
$972$	38.7434	1.24269
$973$	−1.03994	−0.0333389
$974$	88.7465	2.84362
$975$	−116.347	−3.72609
$976$	9.82639	0.314535
$977$	−53.7258	−1.71884	−0.859421	−	0.511269i	$-0.829176\pi$
$977$	−53.7258	−1.71884	−0.859421	+	0.511269i	$0.829176\pi$
$978$	−76.1157	−2.43391
$979$	−3.38269	−0.108111
$980$	−13.0491	−0.416840
$981$	−18.6873	−0.596639
$982$	41.0451	1.30980
$983$	−42.5283	−1.35644	−0.678220	−	0.734859i	$-0.737249\pi$
$983$	−42.5283	−1.35644	−0.678220	+	0.734859i	$0.737249\pi$
$984$	2.54671	0.0811861
$985$	50.7286	1.61635
$986$	22.7380	0.724125
$987$	−44.7973	−1.42591
$988$	−12.9566	−0.412204
$989$	0	0
$990$	17.1236	0.544224
$991$	15.2326	0.483879	0.241940	−	0.970291i	$-0.422216\pi$
$991$	15.2326	0.483879	0.241940	+	0.970291i	$0.422216\pi$
$992$	42.4103	1.34653
$993$	33.1794	1.05292
$994$	−3.92350	−0.124446
$995$	−87.4820	−2.77337
$996$	4.45686	0.141221
$997$	29.8669	0.945894	0.472947	−	0.881091i	$-0.343190\pi$
$997$	29.8669	0.945894	0.472947	+	0.881091i	$0.343190\pi$
$998$	−12.4603	−0.394425
$999$	16.8722	0.533812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.u.1.10		60
23.4	even	11		253.2.i.b.177.10	✓	120
23.6	even	11		253.2.i.b.243.10	yes	120
23.22	odd	2		5819.2.a.t.1.10		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.177.10	✓	120	23.4	even	11
253.2.i.b.243.10	yes	120	23.6	even	11
5819.2.a.t.1.10		60	23.22	odd	2
5819.2.a.u.1.10		60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 5819 = 11 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5819.a (trivial)

\(f(q)\)	\(=\)	\(q-2.05610 q^{2} -2.21869 q^{3} +2.22755 q^{4} -4.33173 q^{5} +4.56186 q^{6} +2.89005 q^{7} -0.467865 q^{8} +1.92260 q^{9} +8.90647 q^{10} +1.00000 q^{11} -4.94225 q^{12} +3.80993 q^{13} -5.94222 q^{14} +9.61078 q^{15} -3.49312 q^{16} -6.41271 q^{17} -3.95307 q^{18} -1.52667 q^{19} -9.64914 q^{20} -6.41213 q^{21} -2.05610 q^{22} +1.03805 q^{24} +13.7639 q^{25} -7.83361 q^{26} +2.39041 q^{27} +6.43772 q^{28} +1.72451 q^{29} -19.7607 q^{30} +5.22427 q^{31} +8.11794 q^{32} -2.21869 q^{33} +13.1852 q^{34} -12.5189 q^{35} +4.28270 q^{36} +7.05826 q^{37} +3.13899 q^{38} -8.45308 q^{39} +2.02667 q^{40} +2.45336 q^{41} +13.1840 q^{42} +2.96049 q^{43} +2.22755 q^{44} -8.32819 q^{45} +6.98634 q^{47} +7.75017 q^{48} +1.35236 q^{49} -28.2999 q^{50} +14.2278 q^{51} +8.48682 q^{52} +1.45325 q^{53} -4.91493 q^{54} -4.33173 q^{55} -1.35215 q^{56} +3.38722 q^{57} -3.54577 q^{58} +13.8389 q^{59} +21.4085 q^{60} -2.81307 q^{61} -10.7416 q^{62} +5.55641 q^{63} -9.70506 q^{64} -16.5036 q^{65} +4.56186 q^{66} +5.36304 q^{67} -14.2846 q^{68} +25.7401 q^{70} +0.660274 q^{71} -0.899520 q^{72} +11.2357 q^{73} -14.5125 q^{74} -30.5378 q^{75} -3.40074 q^{76} +2.89005 q^{77} +17.3804 q^{78} +8.74672 q^{79} +15.1312 q^{80} -11.0714 q^{81} -5.04435 q^{82} -0.901787 q^{83} -14.2833 q^{84} +27.7781 q^{85} -6.08707 q^{86} -3.82616 q^{87} -0.467865 q^{88} -3.38269 q^{89} +17.1236 q^{90} +11.0109 q^{91} -11.5911 q^{93} -14.3646 q^{94} +6.61313 q^{95} -18.0112 q^{96} +2.65813 q^{97} -2.78060 q^{98} +1.92260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) \) 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 + 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 - 7 * q^10 + 60 * q^11 + 41 * q^12 + 46 * q^13 + 16 * q^14 + 4 * q^15 + 99 * q^16 - 5 * q^17 + 36 * q^18 - 8 * q^19 + 82 * q^20 - 13 * q^21 + 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 - 29 * q^28 + 42 * q^29 - 14 * q^30 + 71 * q^31 + 40 * q^32 + 9 * q^33 + 10 * q^34 + 9 * q^35 + 93 * q^36 - 5 * q^37 - 11 * q^38 + 56 * q^39 - 40 * q^40 + 62 * q^41 + 43 * q^42 - 2 * q^43 + 73 * q^44 - q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 - 27 * q^51 + 102 * q^52 + 11 * q^53 + 69 * q^54 + 8 * q^55 + 13 * q^56 + 38 * q^57 + 58 * q^58 + 57 * q^59 - 49 * q^60 - 26 * q^61 + 17 * q^62 - 41 * q^63 + 184 * q^64 - 19 * q^65 + 26 * q^66 + 7 * q^67 - 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 - 63 * q^74 + q^75 - 42 * q^76 - 3 * q^78 - 25 * q^79 + 148 * q^80 + 68 * q^81 + 59 * q^82 - 41 * q^83 - 97 * q^84 + 160 * q^85 + 78 * q^86 + 41 * q^87 + 30 * q^88 + 51 * q^89 - 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 - 13 * q^97 - 75 * q^98 + 75 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more